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\centerline{\large \bf  Traffic flow on road networks}

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\centerline{Benedetto Piccoli}
\centerline{\it IAC - CNR, Rome, Italy }
\centerline{e-mail piccoli@iac.rm.cnr.it  }
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We deal with a simple fluidodynamical model for traffic 
flow on a road network that consists of a conservation law. 
At juctions, rules for traffic distribution must be supplied with a 
flux maximization criterion to obtain uniqueness for the corresponding 
Riemann problem. We construct a semigroup of weak solutions that
satisfy the traffic distribution and  flux maximization rules.
The main problem is the control of total variation. 
Only the total variation of the flux is conserved. Hence, the use of a 
functional counting some big waves is needed. 
Extension to time dependent traffic is illustrated.

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